A Case Study… Constructivism In An Elementary School Math Class This research investigated implications for the implementation of social constructivist epistemology on teaching/learning of mathematics in a K-4 public school with particular focus on African American fourth grade students. In addition, the study examined the impact of social constructivist theory on the structure and culture of the school. Constructivist inquiry was used to make sense of the data. In this paper, there is a discussion of lessons learned from this study with particular emphasis on structural changes, cultural changes, politics of reforming mathematics education, and the impact of social constructivist teaching on African American students' achievement.
There is much research about how students learn mathematics and how mathematics ought to be presented to young children (Burns, 1992; Campbell, 1996; Cobb, Wood, & Yackel, 1991; Cobb & Yackel, 1996; Fennema, Franke, Carpenter, & Carey, 1993; Romberg, Shafer, & Webb, 2000; Simon, 1995; Wheatley & Reynolds, 1999; Yackel, 1995). In addition, research documents indicate that mathematics instruction does not provide students with opportunities to acquire deep mathematical understanding (National Council of Teachers of Mathematics [NCTM], 2000a). A National Science Foundation (NSF, 1996) report indicates fourth grade students in the United States performed better on mathematics proficiency tests of basic skills compared to previous test results. However, the report exposes students' lack of conceptual understanding of those basic skills. Furthermore, current research shows that minority students (i.e., Native Americans, Hispanics, and African Americans) perform well below the national average (Ladson-Billings, 2001; NCTM, 2000b, 2000c; 2001a, 2001b, 2001c). This study communicates the complexity of reforming mathematics education with particular focus on instruction for underachieving African American students. Moses & Cobb (2001) posit that if all students can learn mathematics, then they ought to be provided with opportunities to learn mathematics. Therefore, mathematics literacy is a right rather than a privilege for a few. This study may offer some ideas about how to raise mathematics achievement among African American students who have scored low compared to the average national scores on mathematics achievement tests. This project investigated the following questions: (1) Can social constructivist epistemology be implemented to raise achievement levels of African American students? (2) What impact does social constructivist theory have on the structure and culture of school? And (3) What are the social and political implications for reforming mathematics education in a K-4 elementary school? The research tells the story of a K-4 elementary school that struggled to reform mathematics education (1990-2003) by implementing social constructivist theory and pedagogy in classrooms. After eight years (1990-1998) of focusing on restructuring and recapturing mathematics classrooms, fourth grade students' scores on state mathematics tests dramatically improved for a five year period: 1999-2003. The test results attracted local and statewide attention because African American and white students achieved at about the same high level. In what follows, we describe some history of the reforms in this K-4 school. Then, we discuss our theoretical framework, the design of the study, and lessons learned.
A School History…
The school enrolls 525 students: 60% African American, 34% white, and 6% other racial/ethnic groups. This school is one of five K-4 elementary schools in a Midwest school district that is racially and economically diverse. Eighty-five percent of the teaching staff holds a Master's Degree. The principal, former assistant principal, and two teachers have doctorates in education. The building studied enrolls more students than the other four K-4 buildings in the district and also enrolls the highest percentage of African American students. All the other elementary schools have an African American student population less than 50 percent. About one-half (approximately 150 students) of the African American students in this school come from middle class families. The other half (150 students) of the African American students are from lower middle class or economically disadvantaged families. Ninety percent of the potentially at-risk students are lower middle class or economically disadvantaged African American students. In 1990, school principals (principal and assistant principal, who is now principal in another K-4 elementary school in the same school district) and some teachers led an effort to introduce social constructivist theory in most classrooms. State testing began in 1995. Most of the questions on the fourth grade mathematics test were multiple choice (35 out of 40). Only five questions asked students for written explanations for solving problems. Nearly all test questions asked students to apply skills in the context of relevant mathematics situations. Educators could not easily obtain copies of the test booklets or their students' test responses. Educators were told that the state was not equipped to release classroom sets of students' test booklets. To obtain a specific students test booklet, educators/parents had to write a request and pay to have the test booklet copied (booklets averaged $8.00-$9.00 each). Obtaining a copy of a student’s booklet was not easy. For example, in July 1999, the principals requested 25 booklets of underachieving students. They wanted to analyze students' problem-solving strategies. State officials were reluctant to provide the testing booklets when informed that information from the test was being used for this paper. State Official: We can't release these booklets for research. Students booklets are confidential. Principal: But I am their principal who happens to be conducting a research study about my underachieving students' ability to perform on the proficiency test. How am I going to improve instruction without knowing how these kids did? That is what the state wants, to improve student learning and get all these kids through the test, right? State Official: Well, I need a letter from your superintendent that he is aware of this research study and will guarantee that you have taken precautions about confidentiality of subjects. (Phone conversation, mid-July, 1999)
Educators at this school faced the political pressures of state tests. The publication of test results disturbed the climate of this learning community. In 1998, only 69% of fourth grade students passed the mathematics tests, which was clearly below the 80% average passage rate of other elementary schools in the district. Because of test results, some parents, teachers, school board members, and central office administrators questioned the credibility of the mathematics reform. School principals and teachers searched for ways to blend social constructivist practices with preparation for the state mathematics test. “It's a focused curriculum. Focused on big ideas and on the skills necessary to take those big ideas and apply them to real world situations. The problems that we give the kids are highly contextual. So if you are asking me what makes this different from what you might see in other classrooms, I would think that in other classrooms, mathematics is driven by textbooks. There is no math textbook here” (former assistant principal and current principal of another school in the same school district). Constructivism Yields Positive Results The reform tacked the challenge of closing the achievement gap between white and African American students on the state test. In September 1998 the school principals extended instructional time with "at-risk" students. About 45 third graders and about 40 fourth graders (40% of each grade level) attended extended instructional programs. Instruction was designed according to constructivist learning theory. Main mathematical topics were emphasized as outlined in NCTM Standards (1989, 1991, 1995). Instruction was intentionally active and interactive with learning experiences that stressed writing, speaking, illustrating, building, and role-playing mathematical problems. Before students took the test in March, fourth grade scholars received about 240 extra hours of mathematics tutoring. Parents were urged to enroll their children in these extended programs. As more and more parents noticed and heard about the popularity and effectiveness of these tutoring programs, enrollment grew and most parents praised the school's efforts. Potentially at-risk students were selected and invited based on scores from teacher-made tests, classroom performance, and scores on a third grade Standford Achievement Test (SAT). In addition to closing the achievement gap, the reform confronted the challenge of teaching high level mathematics to all students so that students and educators could meet the goals of a postmodern society. Social constructivism in practice: case study of an elementary school's mathematics program. Publication: Focus on Learning Problems in Mathematics Publish date: January 1, 2005 Author: Pourdavood, Roland; Svec, Lawrence V.; Cowen, Lynn M.
Constructivism In An Elementary School Math Class
This research investigated implications for the implementation of social constructivist epistemology on teaching/learning of mathematics in a K-4 public school with particular focus on African American fourth grade students. In addition, the study examined the impact of social constructivist theory on the structure and culture of the school. Constructivist inquiry was used to make sense of the data. In this paper, there is a discussion of lessons learned from this study with particular emphasis on structural changes, cultural changes, politics of reforming mathematics education, and the impact of social constructivist teaching on African American students' achievement.
There is much research about how students learn mathematics and how mathematics ought to be presented to young children (Burns, 1992; Campbell, 1996; Cobb, Wood, & Yackel, 1991; Cobb & Yackel, 1996; Fennema, Franke, Carpenter, & Carey, 1993; Romberg, Shafer, & Webb, 2000; Simon, 1995; Wheatley & Reynolds, 1999; Yackel, 1995). In addition, research documents indicate that mathematics instruction does not provide students with opportunities to acquire deep mathematical understanding (National Council of Teachers of Mathematics [NCTM], 2000a).
A National Science Foundation (NSF, 1996) report indicates fourth grade students in the United States performed better on mathematics proficiency tests of basic skills compared to previous test results. However, the report exposes students' lack of conceptual understanding of those basic skills. Furthermore, current research shows that minority students (i.e., Native Americans, Hispanics, and African Americans) perform well below the national average (Ladson-Billings, 2001; NCTM, 2000b, 2000c; 2001a, 2001b, 2001c).
This study communicates the complexity of reforming mathematics education with particular focus on instruction for underachieving African American students. Moses & Cobb (2001) posit that if all students can learn mathematics, then they ought to be provided with opportunities to learn mathematics. Therefore, mathematics literacy is a right rather than a privilege for a few. This study may offer some ideas about how to raise mathematics achievement among African American students who have scored low compared to the average national scores on mathematics achievement tests.
This project investigated the following questions: (1) Can social constructivist epistemology be implemented to raise achievement levels of African American students? (2) What impact does social constructivist theory have on the structure and culture of school? And (3) What are the social and political implications for reforming mathematics education in a K-4 elementary school? The research tells the story of a K-4 elementary school that struggled to reform mathematics education (1990-2003) by implementing social constructivist theory and pedagogy in classrooms. After eight years (1990-1998) of focusing on restructuring and recapturing mathematics classrooms, fourth grade students' scores on state mathematics tests dramatically improved for a five year period: 1999-2003. The test results attracted local and statewide attention because African American and white students achieved at about the same high level. In what follows, we describe some history of the reforms in this K-4 school. Then, we discuss our theoretical framework, the design of the study, and lessons learned.
A School History…
The school enrolls 525 students: 60% African American, 34% white, and 6% other racial/ethnic groups. This school is one of five K-4 elementary schools in a Midwest school district that is racially and economically diverse. Eighty-five percent of the teaching staff holds a Master's Degree. The principal, former assistant principal, and two teachers have doctorates in education. The building studied enrolls more students than the other four K-4 buildings in the district and also enrolls the highest percentage of African American students. All the other elementary schools have an African American student population less than 50 percent. About one-half (approximately 150 students) of the African American students in this school come from middle class families. The other half (150 students) of the African American students are from lower middle class or economically disadvantaged families. Ninety percent of the potentially at-risk students are lower middle class or economically disadvantaged African American students.
In 1990, school principals (principal and assistant principal, who is now principal in another K-4 elementary school in the same school district) and some teachers led an effort to introduce social constructivist theory in most classrooms. State testing began in 1995. Most of the questions on the fourth grade mathematics test were multiple choice (35 out of 40). Only five questions asked students for written explanations for solving problems. Nearly all test questions asked students to apply skills in the context of relevant mathematics situations.
Educators could not easily obtain copies of the test booklets or their students' test responses. Educators were told that the state was not equipped to release classroom sets of students' test booklets. To obtain a specific students test booklet, educators/parents had to write a request and pay to have the test booklet copied (booklets averaged $8.00-$9.00 each). Obtaining a copy of a student’s booklet was not easy. For example, in July 1999, the principals requested 25 booklets of underachieving students. They wanted to analyze students' problem-solving strategies. State officials were reluctant to provide the testing booklets when informed that information from the test was being used for this paper.
State Official: We can't release these booklets for research. Students booklets are confidential.
Principal: But I am their principal who happens to be conducting a research study about my underachieving students' ability to perform on the proficiency test. How am I going to improve instruction without knowing how these kids did? That is what the state wants, to improve student learning and get all these kids through the test, right?
State Official: Well, I need a letter from your superintendent that he is aware of this research study and will guarantee that you have taken precautions about confidentiality of subjects. (Phone conversation, mid-July, 1999)
Educators at this school faced the political pressures of state tests. The publication of test results disturbed the climate of this learning community. In 1998, only 69% of fourth grade students passed the mathematics tests, which was clearly below the 80% average passage rate of other elementary schools in the district. Because of test results, some parents, teachers, school board members, and central office administrators questioned the credibility of the mathematics reform. School principals and teachers searched for ways to blend social constructivist practices with preparation for the state mathematics test.
“It's a focused curriculum. Focused on big ideas and on the skills necessary to take those big ideas and apply them to real world situations. The problems that we give the kids are highly contextual. So if you are asking me what makes this different from what you might see in other classrooms, I would think that in other classrooms, mathematics is driven by textbooks. There is no math textbook here” (former assistant principal and current principal of another school in the same school district).
Constructivism Yields Positive Results
The reform tacked the challenge of closing the achievement gap between white and African American students on the state test. In September 1998 the school principals extended instructional time with "at-risk" students. About 45 third graders and about 40 fourth graders (40% of each grade level) attended extended instructional programs. Instruction was designed according to constructivist learning theory. Main mathematical topics were emphasized as outlined in NCTM Standards (1989, 1991, 1995). Instruction was intentionally active and interactive with learning experiences that stressed writing, speaking, illustrating, building, and role-playing mathematical problems. Before students took the test in March, fourth grade scholars received about 240 extra hours of mathematics tutoring. Parents were urged to enroll their children in these extended programs. As more and more parents noticed and heard about the popularity and effectiveness of these tutoring programs, enrollment grew and most parents praised the school's efforts. Potentially at-risk students were selected and invited based on scores from teacher-made tests, classroom performance, and scores on a third grade Standford Achievement Test (SAT). In addition to closing the achievement gap, the reform confronted the challenge of teaching high level mathematics to all students so that students and educators could meet the goals of a postmodern society.
Social constructivism in practice: case study of an elementary school's mathematics program.
Publication: Focus on Learning Problems in Mathematics
Publish date: January 1, 2005
Author: Pourdavood, Roland; Svec, Lawrence V.; Cowen, Lynn M.